The local best mixture of municipal bus and club one in the long run

Unlicensed membership buses have run over the geographical niches only in rush hour in some cities of Brazil. The municipal one then shifts to play the role of satisfying the civil minimum. Some users may think of reserving the membership or not for only the daily use, while they would pay the tax regardless of using the municipal ones. The portion of the two types can equilibrate according to the demands and capacities. We formulate a game model to track the process of market change, and then clarify whether the city may achieve the best mixture of bus service.